Basic Electricity and Calculations (Ugly's / NEC Ch. 9)
Ugly's Electrical References 2020 (Ohm's law, power, series/parallel, voltage drop) · NEC 2020 Ch. 9 (Tables 1, 4, 5, and 8; Notes to Tables) and Annex C · NFPA 72-2022 §7.2.1, §10.6.7.2.1, and Table 14.4.3.2 · Outline tasks 1.1.2, 1.2.2, 1.3.1, 1.1.1
What NICET expects at Level I
At Level I, electrical calculations show up mainly in tasks 1.1.2 (cabling and infrastructure) and 1.2.2 (repair or replace). You are not asked to design but to verify: add up NAC currents, calculate voltage drop, check the voltage at the last appliance, size batteries, and use a multimeter correctly. Tools: the on-screen exam calculator, Ugly's Electrical References, NEC 2020 Chapter 9, and NFPA 72-2022.
Formula sheet
| Concept | Formula | Note |
|---|---|---|
| Ohm's law | E = I × R; I = E ÷ R; R = E ÷ I | Ugly's uses E for voltage |
| Power (watts) | P = E × I = I² × R = E² ÷ R | Ugly's formula "wheel" |
| Resistors in series | RT = R1 + R2 + ... | The same current flows through the whole loop |
| Resistors in parallel | 1/RT = 1/R1 + 1/R2 + ...; equal values: R ÷ n | The same voltage across each branch |
| Kirchhoff (currents) | IT = I1 + I2 + ... | Total current of a NAC |
| Kirchhoff (voltages) | E source = sum of drops | V at last appliance = starting V − VD |
| DC voltage drop, 2-wire (K method) | VD = 2 × K × I × L ÷ CM | K = 12.9 copper, 21.2 aluminum (Ugly's); L = one-way distance |
| Voltage drop (resistance method) | VD = I × (Ω/kft × 2L ÷ 1000) | Ω/kft from NEC Ch. 9, Table 8 |
| Three-phase drop (Ugly's) | VD = 1.732 × K × I × L ÷ CM | Rarely used in fire alarm |
| Batteries | Ah = (I standby × 24 h) + (I alarm × 5/60 h), then × margin | NFPA 72-2022 §10.6.7.2.1; EVACS: 15/60 h |
Prefixes: 1 mA = 0.001 A; 1 kΩ = 1000 Ω; 1 MΩ = 1,000,000 Ω; 1 mW = 0.001 W. Always convert mA to A before multiplying. 5 min = 0.0833 h; 15 min = 0.25 h.
NEC 2020 Ch. 9, Table 8: values to keep handy
DC resistance at 75°C (167°F), uncoated copper, in ohms per 1000 ft. Values checked against Table 8; for these sizes they have not changed in recent NEC editions.
| AWG | Area (cmil) | Solid (Ω/kft) | Stranded, 7 strands (Ω/kft) |
|---|---|---|---|
| 18 | 1620 | 7.77 | 7.95 |
| 16 | 2580 | 4.89 | 4.99 |
| 14 | 4110 | 3.07 | 3.14 |
| 12 | 6530 | 1.93 | 1.98 |
| 10 | 10,380 | 1.21 | 1.24 |
Coated copper has slightly higher resistance (for example, 14 AWG stranded coated = 3.26 Ω/kft). Quick rule: smaller AWG number = thicker conductor = less resistance = less voltage drop.
Worked example: NAC voltage drop
24 VDC NAC with a 1.8 A total load; last appliance 250 ft away (one way); 16 AWG stranded cable; appliances listed for 16–33 VDC; the manufacturer says to start from 20.4 V (85% of 24 V, battery at end of discharge).
- Loop length: 2 × 250 ft = 500 ft = 0.5 kft.
- Loop resistance: 4.99 Ω/kft × 0.5 kft = 2.495 Ω.
- VD = 1.8 A × 2.495 Ω ≈ 4.49 V. With the K method: 2 × 12.9 × 1.8 × 250 ÷ 2580 = 4.50 V.
- Voltage at the last appliance: 20.4 − 4.49 = 15.91 V → does not comply (below 16 V).
- With 14 AWG stranded: 3.14 × 0.5 = 1.57 Ω; VD = 1.8 × 1.57 ≈ 2.83 V; 20.4 − 2.83 = 17.57 V → complies.
The lumped-load method (all current at the end of the circuit) is conservative: if it passes this way, it also passes a point-to-point calculation. The acceptance criterion is the appliance's listed operating range from the manufacturer, not an NFPA 72 number.
Worked example: batteries
Total standby current 0.320 A; total alarm current 2.75 A; non-voice system.
- Standby: 0.320 A × 24 h = 7.68 Ah.
- Alarm: 2.75 A × (5 ÷ 60) h ≈ 0.229 Ah.
- Subtotal: 7.68 + 0.229 ≈ 7.91 Ah.
- 25% capacity margin (factor 1.25): 7.91 × 1.25 ≈ 9.89 Ah. With the 20% of earlier editions it would be ≈ 9.49 Ah.
- Choose the next commercial battery size the panel charger can recharge (for example, 12 Ah). Two 12-V batteries in series give 24 V with the same Ah capacity.
EOL, supervision, and typical readings
On Class B, the end-of-line (EOL) resistor goes at the last device on the circuit; the panel watches a small supervisory current (for example, 24 V ÷ 4.7 kΩ ≈ 5.1 mA). The wire must go in and out of each terminal, with no T-taps on conventional circuits, and the wire run must be broken at each terminal rather than looped under it. In standby a NAC supervises with reversed polarity and polarized appliances block that current, so + and − must be respected. Readings with the circuit disconnected from the panel:
| Condition | Between the two conductors | Conductor to ground |
|---|---|---|
| Normal | ≈ EOL value + wire (e.g., 4.72 kΩ) | Very high (MΩ or OL) |
| Open | OL (infinite) | Very high |
| Short or closed contact | A few ohms (wire only) | Very high |
| Ground fault | Normal | Low |
A wrong EOL (47 kΩ instead of 4.7 kΩ) cuts the supervisory current to one-tenth and the panel may see it as an open. Two equal EOLs in parallel give half the value.
Multimeter and megohmmeter
- Voltage: in parallel, across the component (for example, at the terminals of the last appliance with the NAC in alarm).
- Current: in series, opening the circuit and using the A/mA input. Never across the power source.
- Resistance and continuity: only with the circuit de-energized and disconnected from the panel.
- Megohmmeter: applies high dc voltage to measure insulation in MΩ; disconnect the panel and all devices before testing.
- Tests of new conductors (NFPA 72-2022, Table 14.4.3.2): maximum stray voltage of 1 V ac/dc unless the manufacturer specifies otherwise; insulation to ground; insulation between conductors; loop resistance (pair shorted at the far end) within the manufacturer's limit.
Alternating current and distribution systems
In the U.S., ac is 60 Hz. Common systems in Ugly's: single-phase 120/240 V (120 V hot to neutral, 240 V between hots), three-phase 208Y/120 V (208 ÷ 1.732 ≈ 120 V to neutral), and 480Y/277 V. The fire alarm panel is normally fed with 120 V ac (hot and neutral; never use the equipment grounding conductor as a return) and supplies 24 V dc to its circuits; the batteries are dc.
Conduit fill (NEC Ch. 9)
| Case | Maximum | Where |
|---|---|---|
| 1 conductor (or 1 multiconductor cable) | 53% | Table 1 + Note 9 |
| 2 conductors | 31% | Table 1 |
| More than 2 conductors | 40% | Table 1 |
| Nipple of 24 in. (600 mm) or less between boxes | 60% | Note 4 |
Same-size conductors: Annex C (Table C.1 = EMT). Mixed sizes: add the areas from Table 5 (14 AWG THHN = 0.0097 in²; 12 AWG THHN = 0.0133 in²) and compare with the matching column of Table 4 (1/2 in. EMT at 40% = 0.122 in²). Round up only if the decimal is 0.8 or more (Note 7).
NFPA 72 does not set a color code for fire alarm conductors: follow the project drawings and specifications.
- Forgetting the × 2 (out and back) in voltage drop, or applying it twice.
- Using mA as if they were A.
- Using 5 minutes as 5 hours (5 ÷ 60 = 0.0833 h).
- Confusing solid with stranded, or coated with uncoated, in Table 8.
- Using 31% when there are more than 2 conductors.
- Believing that changing the EOL fixes voltage drop.
- Measuring current with the meter in parallel.
- Accepting an appliance that "works" at a voltage below its listed range.
How to find it fast in the printed books
- NEC: Chapter 9 tables follow Chapter 8 near the back of the book, just before the Informative Annexes. Tab Table 1 together with the Notes to Tables (Notes 4, 7, and 9 are on the same pages), Table 4, Table 5, and Table 8 (Conductor Properties). Tab Annex C at Table C.1 (EMT); the annex is organized by raceway type.
- NFPA 72: in the index, look up "Batteries," "Power supplies, secondary," and "Documentation." Tab §10.6.7 for battery capacity (§10.6.7.2.1), §7.2.1 for the minimum documentation (battery and voltage drop calculations), and Table 14.4.3.2 for conductor and battery tests (stray voltage, loop resistance).
- Ugly's: use the table of contents to tab Ohm's Law / Power Formulas, Series and Parallel Circuits, and Voltage Drop Calculations.
What to tab in your books
| Section | Why |
|---|---|
| NEC 2020 Ch. 9, Table 8 | Conductor properties: cmil and dc resistance at 75°C (Ω/kft), solid and stranded |
| NEC 2020 Ch. 9, Table 1 | Percent fill: 1 conductor 53%, 2 conductors 31%, over 2: 40% |
| NEC 2020 Ch. 9, Notes to Tables | Note 4 (nipples ≤ 24 in.: 60%), Note 7 (round up at ≥ 0.8), Note 9 (multiconductor cable = 1 conductor) |
| NEC 2020 Ch. 9, Table 4 | Conduit and tubing dimensions and areas by type (EMT, PVC, RMC...) at 40/53/31/60% |
| NEC 2020 Ch. 9, Table 5 | Dimensions and areas of insulated conductors (THHN, TFFN...) |
| NEC 2020 Ch. 9, Table 9 | AC resistance and reactance (do not confuse with Table 8, dc) |
| NEC 2020 Annex C | Maximum number of same-size conductors per raceway (C.1 = EMT) |
| Ugly's 2020 – Ohm's Law / Power Formulas | E, I, R, P formula wheel |
| Ugly's 2020 – Series and Parallel Circuits | Resistance, current, and voltage in series and in parallel |
| Ugly's 2020 – Voltage Drop Calculations | VD = 2 × K × I × L ÷ CM (1φ) and 1.732 × K × I × L ÷ CM (3φ); K = 12.9 Cu, 21.2 Al |
| Ugly's 2020 – distribution systems | 120/240 V single-phase, 208Y/120 V, and 480Y/277 V |
| NFPA 72-2022 §10.6.7.2.1 | Secondary capacity: 24 h standby + 5 min alarm (15 min for EVACS) |
| NFPA 72-2022 §7.2.1 | Minimum documentation: battery and NAC voltage drop calculations |
| NFPA 72-2022 Table 14.4.3.2 | Conductor tests (1 V stray voltage, ground, short, loop resistance) and battery tests |
| NFPA 72-2022 §10.3 | Equipment listed, installed per the manufacturer, and compatible |
| NFPA 72-2022 Ch. 12 | Circuits and pathways: Class A/B, monitoring for integrity, ground faults |
Chapter vocabulary
- Voltage (E)
- Electrical potential difference, measured in volts (V) with the voltmeter in parallel.
- Current (I)
- Flow of electric charge, measured in amperes (A) with the ammeter in series.
- Resistance (R)
- Opposition to current flow, measured in ohms (Ω) with the circuit de-energized.
- Ohm's law
- The relationship E = I × R between voltage, current, and resistance.
- Power (P)
- Energy per unit of time, in watts: P = E × I = I² × R = E² ÷ R.
- Series circuit
- A single current path; resistances add and the current is the same throughout the loop.
- Parallel circuit
- Several branches with the same voltage; branch currents add (like the appliances on a NAC).
- Voltage drop (VD)
- Voltage lost in conductor resistance: VD = I × R of the complete loop.
- Circular mil (cmil)
- Unit of conductor area used in NEC Table 8 (14 AWG = 4110 cmil).
- Stranded conductor
- Conductor made of several strands; for the same AWG it has slightly more resistance than solid wire.
- End-of-line (EOL) resistor
- Resistor installed at the end of a Class B circuit so the panel can supervise the wiring.
- Supervisory current
- Small current that flows through the EOL in standby; if it moves outside its window, the panel indicates trouble.
- Open circuit
- A break in the current path; the ohmmeter reads OL (infinite).
- Short circuit
- Low-resistance connection between conductors that bypasses the load or the EOL.
- Ground fault
- Unintended connection of a circuit conductor to ground (conduit, box, structure).
- Stray voltage
- Unwanted voltage on installation conductors; NFPA 72 limits it to 1 V ac/dc in acceptance testing.
- Megohmmeter (insulation tester)
- Instrument that applies a high dc voltage to measure insulation resistance in MΩ.
- Multimeter (DMM)
- Instrument that measures voltage, current, and resistance depending on the function and inputs selected.
- Ampere-hour (Ah)
- Battery capacity: the current multiplied by the time the battery can deliver it.
- Secondary power supply
- Batteries (or another approved source) that keep the system operating when primary power fails.
- Quiescent load
- Current the system draws in its normal condition, without alarm.
- Lumped load
- Calculation method that assumes all NAC current is drawn at the last appliance; gives a conservative result.
- Conduit fill
- Percentage of a raceway's interior area occupied by conductors or cables (NEC Ch. 9, Table 1).
- Alternating current (ac)
- Current that periodically reverses direction; 60 Hz in the U.S.
- Nipple
- Short length of conduit (24 in. or less) between boxes or enclosures; may be filled to 60%.
50 practice questions cover this chapter, each with an explanation and the code section. Get lifetime access or try the free practice exam.
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- Initiating Devices
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- Circuits, Systems, and Control Functions
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- Basic Electricity and Calculations
- Inspection, Testing and Maintenance
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